Given the table below, which of the following statements is true?

Line Equation
Line A y=−12x−2
Line B y=2x−3
Line C y=12x+2
Line D y=2x+5



(1 point)
Responses

Line C is perpendicular to Line D
Line C is perpendicular to Line D

Line B is perpendicular to Line D
Line B is perpendicular to Line D

Line A is perpendicular to Line C
Line A is perpendicular to Line C

Line A is perpendicular to Line B
Line A is perpendicular to Line B
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1 answer

To determine which statements are true regarding the perpendicularity of the given lines, we need to look at the slopes of each line from their equations.

  1. Line A: \(y = -12x - 2\)

    • Slope (m) = -12
  2. Line B: \(y = 2x - 3\)

    • Slope (m) = 2
  3. Line C: \(y = 12x + 2\)

    • Slope (m) = 12
  4. Line D: \(y = 2x + 5\)

    • Slope (m) = 2

Two lines are perpendicular if the product of their slopes equals -1.

Now we can evaluate the pairs given in the statements:

  • Line A (slope -12) and Line B (slope 2): \[ -12 \times 2 = -24 \quad (\text{not perpendicular}) \]

  • Line A (slope -12) and Line C (slope 12): \[ -12 \times 12 = -144 \quad (\text{not perpendicular}) \]

  • Line B (slope 2) and Line D (slope 2): \[ 2 \times 2 = 4 \quad (\text{not perpendicular}) \]

  • Line C (slope 12) and Line D (slope 2): \[ 12 \times 2 = 24 \quad (\text{not perpendicular}) \]

Since none of the pairs produce a product of -1, none of the statements about perpendicularity among the lines provided is true.

Therefore, all the statements provided are false.